Pistol?

I have seen some pretty neat looking bolt action jobs with heavy barrels, maybe 16 inches(?), and a bipod. I know essentially nothing about it, but thought it might be fun to set up a pistol for shots over 500 yards.

How would you set up a pistol for 'yotes? Caliber? Action? Stock? Scope?

I have a T/C Contender in 7x30 Waters and just got a SSK barrel chambered in 6.5JDJ which is a 225 Win case necked up to .264" and a 40 deg shoulder. It shoots a 120 gr BT at 2400 fps and is a 300 yd deer gun. I got it sighted in at 100 yds last weekend and will get serious with it this spring.

Coyotes to 500 yards with specialty handguns is not to much of a problem as far as hitting them. The key of course is getting the bullet to perform the way you want at varying distances.
I would opt for a bolt pistol before a break-open but that is preference on my part.
You are going to shoot approximately 200-300 fps slower in a specialty handgun than you do in a rifle.
If you want 243 Win performance consider a 6-284.
If you want 6.5-284 performance go with a 6.5WSM.
My hunting buddy Steve Hugel (sscoyote) longest shot on a yote was just over 900 yards. He has made a # of other kills in the 350-600 yard range with pistols.
In SP's he has a 17 Mach IV, 20BR, (soon to be)6.5WSM, and 7mmx270WSM. These are not just for coyote but PD's and big game.
My rigs are: 22-250AI, 260 Rem, 250 Sav.AI.
My main LR rigs are: 6mm-284, several 6.5-284's, and a soon to arrive a 7T Lilja 7mm Dakota.
The 6-284, two of the 6.5-284's and the Dakota are XP-100's (1 rear-grip 6.5-284 and all the rest are center-grip).

I built a long range pistol. I used a Rem SA. It is a forward grip design and has a Dell Taylor trigger (highly reccomended). I milled the stock out of aluminum and it may be used with a bipod although I currently havn't yet. Most people would use a handgun scope or at least some sort of extended eye relief scope but I put an IOR 4-14 tactical on it because I cannot stand handgun scopes and I really like that IOR scope. Cartrige is a 338-300WSM utilizing the 300gr SMK out of a 9"twist 15.5inch mike rock barrel.

If you don't get many more replies do a search and you should find some other info that members have posted.